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10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13 Delft, The Netherlands, July 2-4, 2013

3D organization of high-speed compressible jets by tomographic PIV

D. Violato1, G. Ceglia2, M. Tuinstra3 and F. Scarano1

1

Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg,1, 2629 HS, Delft, the Netherlands, d.violato@tudelft.nl

2

DIAS, Università degli Studi di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy 3

National Aerospace Laboratory, Voorsterweg 31, 8316 PR Marknesse, The Netherlands

ABSTRACT

This work investigates the three dimensional organization of compressible jets at high-speed regime by tomographic particle image velocimetry (TOMO PIV). Experiments are conducted at Mach numbers 0.3, 0.9 and 1.1 (under-expanded regime) across the end of the potential core within a large cylindrical domain (1.6Dx8D, with D=22mm the jet diameter). At M=1.1, shock and expansion waves are observed in the potential core between Z/D=2.6 and Z/D=5. The velocity fields are analysed by proper orthogonal decomposition (POD) to investigate the three-dimensional organization of large scale structures. Modal patterns are described based on visualizations of the axial velocity, which, among the velocity components, is the main contributor to the total fluctuating kinetic energy. Azimuthal Fourier decomposition is performed prior to POD to reduce the measurement noise of the extracted modes. At any Mach number, the most energetic modes show energy peaks by the end of the potential core and beyond (Z/D>5). At M=1.1, shock and expansion waves are not detected in the most energetic modes.

INTRODUCTION

The turbulent structure of jets at high Reynolds numbers have been largely investigated in relation to several engineering applications, as well as in the framework of fundamental studies on turbulence. The aeroacoustic behavior of high-speed subsonic and supersonic jets is particularly relevant both in aeronautics as well in a number of engineering applications where the mass flow is maximized by operating the jet in the under-expanded regime.

The knowledge of the large-scale patterns, being a prominent noise sources (Jordan and Colonius, 2013), represents a crucial step to venture investigations on the noise generation process. Studies have been conducted with DNS and LES simulations (Freund, 2001; Bogey et al., 2003; Boersma, 2005) whereas, experimentally, they have been commonly conducted by hotwire anemometry and planar PIV in combination with modal decomposition.

Jung et al. (2004) scanned the first 6 diameters of a turbulent incompressible jet at high Reynolds number with a polar array of 138 synchronized straight hot wire probes and showed a low-dimensional time-dependent reconstruction of the streamwise velocity using the dominant modes retrieved by proper orthogonal decomposition (POD, Sirovich, 1987). Reconstruction of the full-field streamwise velocity component using the dominant POD modes shows clearly the evolution of the flow with downstream position, from ‘volcano-type’ eruptions to a ‘propeller-like’ pattern. In a later study at Re=3.8 105 and Mach 0.3, Iqbal and Thomas (2007) achieved a three component implementation of the POD analysis and reported a helical vortex structure beyond the tip of the potential core of jet.

With stereo PIV and microphone measurements, Alkislar et al.(2007) studied the effect of streamwise vortices on the aeroacoustics of a Mach 0.9 axisymmetric jet using two different devices to generate streamwise vortices: microjets and chevrons. Large-scale patterns in compressible regime were also investigated by Tinney et al. (2008) who, in a Mach 0.85 axisymmetric jet, extracted the POD modes from stereo PIV cross-sectional realizations and showed the mechanism of fluid entrainment with low-order reconstructions of the velocity field. In a later study, the authors (Tinney et al., 2008b) acknowledged the use of volumetric measurement techniques for aeroacoustic studies as, contrarily to planar or point-wise ones, they enable to provide unambiguous interpretations of the 3D flow patterns.

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In previous studies by Violato and Scarano (2011, 2013) the use of tomographic PIV ( TOMO PIV, Elsinga et al., 2006) has been made to capture the relation between the instantaneous turbulent structures and the activity of the acoustic source. However, the works dealt with jets in the incompressible regime and at low Reynolds number (Re=5,000). On the other hand, it was possible to elucidate the statistical relation between large scale fluid modes and the modes associated to sound production by a careful inspection of the patterns produced by POD.

In the present investigation, TOMO PIV experiments are conducted on high-speed turbulent jets operated at high Reynolds up to the transonic regime. The three dimensional velocity data are analyzed by POD technique to deduce of the flow patterns corresponding to the most energetic fluctuations. The ultimate objective of this study is to determine to what extent the compressibility effects should be taken into account for the treatment of the sound source when large flow scales are concerned.

PROPER ORTHOGONAL DECOMPOSITION

Proper Orthogonal Decomposition (POD) is a statistical technique to objectively classifying and describing turbulent flows in terms of most energetic coherent motions that can be used to produce of a low-order reconstruction of the flow field. When applied to velocity fields, such as PIV data or numerical simulations, POD analysis enables the identification of the coherent structures in terms of global eigenmodes. POD was applied to planar PIV data to describe a large variety of jet flow configurations (Violato and Scarano, 2013). In transitional jets, Violato and Scarano (2013) showed that POD is a powerful tool to describe the 3D flow coherence when applied to TOMO PIV data.

The POD principles is applied following the method of snapshots (Sirovic, 1987). Consider a set of data u( , )xtn that are simultaneously taken at N time instants such that the samples are uncorrelated and linearly independent. The corresponding fluctuating component is defined as

'( , )n ( , )n ( )

u xt =uxtu x

, (1)

where u x( ) is the temporal average

The POD method extracts orthonormal eigenmodes

ψ

( )x and orthonormal amplitude coefficients a tk( ) such that the

reconstruction 1 '( , )n k( ) k( ) k u t a tψ ∞ = =

x x (2)

is optimal, in the sense that the functions

ψ

maximize the normalized average projection of

ψ

onto u'

( )

(

)

(

)

2 ( ), ' , max ( ), ( ) u t ψ

ψ

ψ

ψ

x x x x . (3)

The time coefficients

a t

k

( )

are determined by the projection of the flow-fields on the global modes

( )

(

)

( ) ' , , ( ) k k a t = u x t

ψ

x . (4)

The snapshot method introduced by Sirovic (1987) is less computationally demanding and the above maximization problem corresponds to solve a degenerate integral equation, in which the solutions are linear combinations of the snapshots 1 ( ) '( , ) 1, ..., N k k n n n u t k N ψ = =

Φ = x x (5) where k n

Φ

is the nth component of the kth eigenvector. The eigenmodes can then be found by solving the following eigenvalue problem

u

CΦ = Φ

λ

(3)

where C is the L2-norm matrix,

(

)

1 '( ), '( ) u C u u N = x x . (7)

The cumulative sum of the eigenvalues

λ

k corresponds to the total energy and each eigenmode is associated with an

energy percentage

e

k: 1 N k k i i e λ λ = =

. (8)

POD descriptions of PIV data are commonly produced choosing the mean square fluctuating velocity as norm, which represents the kinetic energy of the flow.

In this investigation, POD analysis is first conducted on three-dimensional velocity data sets based on the mean square fluctuating energy (eq. (1)), which, for the fluctuating velocity vector (V') can be written as

(

)

1 '( ), '( ) V C N = V x V x (9)

Alternatively, azimuthal Fourier decomposition is applied assuming periodic properties of the flow along the azimuthal coordinate (Colonius 2002, Tinney et al. 2008). After being transformed into cylindrical coordinates (z,r,θ), the velocity field is decomposed

( )

/2 /2 ( , , , ) ( , ) , , m N m im m N u z r t u z r u z r t e θ θ θ

θ

= =− = +

(10) and then POD modes are computed for each Fourier mode m as

( )

, , ( ) ( , ) 0,..., m m m k k N k u z r t =

a t

ψ

z r m= Nθ . (11)

EXPERIMENTAL APPARATUS AND PROCEDURES

Jet flow facility

The experiments are conducted in the jet tomography facility the Aerodynamic Laboratories of TU Delft in the Aerospace Engineering Department. Tests are conducted on a contoured shaped nozzle, with exit diameter is D=22 mm and contraction ratio of 4.4:1 are installed at the bottom wall of the Jet Tomography Facility (JTF) developed in previous works (Violato and Scarano, 2011). The nozzle is connected to a support, which, as shown in Figure 1, is divided in a settling chamber (a) and a pressure chamber (c) by a choke plate (b) with diameter of 100 mm. In the pressure chamber, the total pressure P0 and the total temperature T0 are measured by means of a static pressure tube and

a thermocouple, respectively. The maximum pressure allowed in this chamber is approximately of 30 bar. The high pressure system provides stabilized air supply with mass flow rate up to 0.15 Kg/s and pressure of approximately 3 bar in the pressure chamber. The pressure drops due to the filters and choking plate are found to be about 1 bar at Mach number 0.9. Causing the liquefaction of the PIV seeding, the metallic foam material (retimex) used to reduce the turbulence level is removed. A wooden extension of 1.6 m is applied on the Plexiglas tank, as shown in Figure 2.

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Measurements are performed at Mach 0.3, 0.9 and 1.1 (under-expanded regime). The exit velocity Wj are, respectively,

100 m/s, 270 m/s and 340 m/s, corresponding to Reynolds numbers of 160,000, 400,000 and 600,000 based on the jet diameter.

While the statistical characterization is conducted by planar PIV (2C-PIV) and is discussed in Ceglia et al. (2013), this study focuses on tomographic PIV experiments.

Figure 2 Schematic view experimental arrangement for tomographic PIV measurements (top); top view of the system (right).

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Tomographic PIV measurements

The flow is seeded with DEHS particles (particle diameter of 1 micron) in a concentration of 0.86 particles/mm3. Laser pulses are produced with a double-cavity Spectra-Physics Quanta Ray Nd:YAG system (532 nm, 400mJ/pulse, 6 ns pulse duration). After a transmission distance of approximately 4 m, the laser beam features a diameter of 6 mm and is further expanded through a beam expander to a diameter of 35mm. At the top of the wooden extension, as shown in Figure 2, a Plexiglas window enables the access of the laser light. About 100 mm upstream of the window, a cross-jet of air is placed to avoid the deposit of impurities (mainly PIV seeding particles).

The illumination is provided by the laser. The light scattered by the particles is recorded by a tomographic system composed of four LaVision Imager Pro LX 16M (4872x3248 pixels, pixel pitch 7.4µm) at frequency of 1.7 Hz. The cameras are arranged horizontally with azimuthal aperture of 90 degrees (Figure 2). The shape of the illuminated volume with a beam of cylindrical cross section eliminates the need for camera-lens tilt mechanism to comply with the Scheimpflug condition. Nikon objectives of 105mm focal length are set with a numerical aperture f#=16 to allow focused imaging of the illuminated particles. For the chosen imaging configuration and for the selected particle concentration, the particle image density attains a maximum of 0.04particles/pixel at the jet axis and decreases towards the edge of the illuminated volume. The separation time between the two exposures is set to obtain a maximum displacement of approximately 12 pixels along the jet axis exit. The field of view is of 1.6Dx8D (35x190mm2) with a digital resolution of 25 pixels/mm. The measurement domain extends from 2.6 diameters off the nozzle. The details of the experimental parameters are summarized in table 1.

Table 1 Experimental parameters

Seeding diameter [µm]

concentration [particles/mm3]

1 0.86 Illumination Spectra-Physics Quanta Ray double

cavity Nd:Yag laser (2 x 400mJ@10Hz)

beam diameter 35 mm Recording device LaVision Imager Pro LX 16M

cameras (4872x3248 pixels@ 3Hz) 4 cameras Optical arrangement Nikon objectives ( f ; f#)

field of view 105mm; 16 1.6D x 8D Magnification 0.18 Acquisition frequency 1.7Hz Pulse separation: M=0.3, M=0.9 M=1.1 5 µs 1.5 µs 1.5 µs Number of recorded images 500

The volumetric light intensity reconstruction is performed combining the MLOS technique with the SMART algorithm by the LaVision software Davis 8. This method allows to reduce the time of 3D light intensity reconstruction by factor 5 compared to the standard MART technique. A three-dimensional mapping function from image-space to physical object-space is generated by imaging a calibration target. The initial experimental errors due to system calibration are approximately 0.5 pixels as estimated from the disparity vector field. The misalignment is reduced to less than 0.05 pixels making use of the 3D self-calibration technique (Wieneke, 2008). The raw images are pre-processed with subtraction of the minimum intensity at each pixel for the entire sequence, followed by a subtraction of the local minimum over a kernel of 31x31 pixels. The SMART algorithm is applied with five iterations, without compromising the reconstruction accuracy in comparison to MART. The illuminated volume is discretized with 1135 x 4731 x 1141 voxels.

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The three-dimensional particle field motion is computed with volume cross-correlation technique by the LaVision software Davis 8. A final interrogation volume of 80x80x80 voxels (2x2x2 mm3) with an overlap between adjacent interrogation boxes of 75% produce a velocity field measured over a grid of 57 x 57 x 237 points (vector pitch of 0.5 mm). At the given particle concentration, 9 particles are counted, on average, within the interrogation box.

Data processing is performed on a 48-core Intel Xeon processor at 2.20 GHz with 132 GB RAM memory. Reconstruction of a pair of objects and the 3D cross-correlation requires 40 minutes and 20 minutes respectively. Planar PIV measurements are also performed on the jet.

The statistical characterization of the jet flow has been conducted by planar PIV of which a detailed discussion is given in Ceglia et al. (2013).

RESULTS

Instantaneous 3D velocity fields

The instantaneous flow organization is shown in Figure 3, where jet flows jet M=0.3, 0.9 and 1.1 are illustrated by iso-surfaces of axial velocity component W. More detailed information on the shear layer can be retrieved from Figure 4, which shows the cross-sectional iso-contour of W extracted from plane y/D=0 and compares it with the measurements obtained by planar PIV measurements (a-c, Ceglia et al. 2013).

M=0.3 M=0.9 M=1.1

a) b) c)

Figure 3 High-speed-jet velocity; iso-surface of axial velocity components and velocity vectors (shown 1 every 10 along Z-axis)

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Note that TOMO PIV extends from 2.6 jet diameters off the nozzle to Z/D=10.6. Although the tomographic measurements are noisier than to the planar ones with spatial resolution reduced by a factor 3, the tomographic data still provide a good description of the large-scale events.

M=0.3 M=0.9 M=1.1

a) b) c)

d) e) f)

Figure 4 Iso-contours of axial velocity component; planar PIV data (a-c) and tomographic PIV data on plane y/D=0 (d-f).

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Figure 3 and Figure 4 show the axial development with patches of higher axial velocity that are more evident across the end of the potential core (5<Z/D<8). At M=1.1 such regions, which are produced by a sequence of shock/expansion waves (Ceglia et al., 2013), are detected starting from the nozzle exit.

Modal decomposition

The analysis of the related 3D patterns is aided by POD analysis of the velocity field V to retrieve objective descriptions of the large-scale features which are hardly detectable by simple visual inspection. Special care is given to characterize the region by the end of the potential core, which is a prominent acoustic source.

POD decomposition of velocity is based on a sequence of 100 uncorrelated snapshots following the method of snapshots (eq (9)). The distribution of energy across the three-dimensional POD modes and the cumulative energy distributions are illustrated in Figure 5 for each Mach number. At M=1.1 and M=0.9, the first 20 modes capture an energy percentage larger than at Mach 0.3, with the first two modes that capture approximately 5.7% of the total fluctuating kinetic energy.

Figure 5 Left: energy distributions across first 20 POD modes k of velocity; right: cumulative energy distributions (symbols are shown 1 every 5)

POD modes are analyzed in terms of axial velocity component W since this is the component that contributes with largest amount of fluctuating kinetic energy. Mode k=1 is illustrated in Figure 6. At M=0.3, the first pair (k=1 and k=2) is phase shifted of approximately 90 degrees about the jet axis, describing a precession motion. This was also reported for mode pair #9-#10 in the Re=5,000 jet investigated by Violato and Scarano (2013). At M=0.9 and 1.1, the first pair is phase shifted of π/2 in the axial direction, describing travelling waves. The intertwining between the region of positive and negative W indicates a helical motion (Iqbal and Thomas, 2007). For Z/D>8, instead the first pair identifies a flapping motion, as reported for incompressible jets by (Lynch and Thurow, 2009; Violato and Scarano, 2013).

The most energetic modes (Figure 6) as well as those at higher k-number are affected by noise. A possible strategy to reduce the noise level on the POD modes is to first treat the velocity fields with the azimuthal Fourier decomposition and then apply POD (equations (10) and (11)). Figure 7 shows the energy distribution among the POD modes k extracted for each azimuthal Fourier mode m.

For all the Mach numbers herewith analysed, the most energetic mode is the first POD mode k=1 extracted from Fourier mode m=1. For clarity it will be referred to as (k=1, m=1). At M=0.3 and 0.9, it captures 2.7% of the total energy whereas it is associated with 3.2% of the total energy at M=1.1. As shown in Figure 8, positive and negative W describe a swirling pattern that grows from the region across the end of the potential core till the downstream limit of the measurement domain (Z/D=10.6). At M=0.3 the mode develops with a spatial wavelength of 5 jet diameters starting from Z/D=6 while it has a spatial wavelength of 6 jet diameters at M=0.9 starting from Z/D=5. At M=1.1, instead, the swirling pattern develops from Z/D=5 with a wavelength of 3 jet diameters. The most energetic mode of M=1.1 jet shows no evidence of shock and expansion patterns in the region between 2.6<Z/D<5, as, instead observed in the instantaneous velocity iso-contours (Figure 4) and in the cross-correlation analysis discussed by Ceglia et al. (2013).

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Peak of energy is observed at mode (k=1, m=2) for all the investigated regimes (Figure 7). At M=0.3, as shown in Figure 8, two filaments of positive and negative W describe a characteristic pulsatile motion, developing from Z/D=2.6 and showing a intertwining of the filaments by the end of the potential core (Z/D=7), pattern that was previously reported in the incompressible jet investigation by Violato and Scarano (2013). At the higher regimes, mode (k=1, m=2) depicts a swirling pattern similar to mode (k=1, m=1) with a 90 degrees rotation around the jet axis. At M=0.9 the wavelength is the same, whereas at M=1.1 it is 4 jet diameters.

M=0.3 M=0.9 M=1.1

Figure 6 First POD mode of velocity describing travelling waves. Positive (light grey) and negative (dark grey) iso-surfaces of axial velocity components.

M=0.3 M=0.9 M=1.1

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M=0.3 M=0.9 M=1.1

k=1; m=1

k=2; m=1

Figure 8 First and second POD mode of azimuthal mode m=1. Iso-surfaces of positive (yellow) and negative (blue) axial velocity component W.

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Axisymmetric modes describe axial pulsatile motions. At any Mach number herewith investigated, mode (k=1; m=1) is characterized by decelerations beyond the end of the potential core (Figure 9) whereas axial acceleration are typical of the mixing layer around the potential core.

The three dimensional features of modes (k=1, m=2) and (k=2, m=2) are depicted in Figure 10. Mode (k=1, m=2) shows the axial development of four filaments of W, two of positive and two negative sign, that grow from upstream the end of the potential core (Z/D=5). A swirling pattern is reported for M=0.3 between Z/D=2.6 and 5, which instead decays at M=0.9 and is absent at M=1.1. At M=0.3, mode (k=2, m=2), as shown in Figure 10, describe a pattern similar to (k=1, m=2) with 45 degrees shift around the jet axis. At M=0.9, on the other hand, it shows the presence of three regions along the jet axis (4.5<Z/D<6; 6<Z/D<8; 8<Z/D<10.6) which, with respect to each other, are shifted of 90 degrees around the jet axis. At M=1.1, the same mode describes an axial swirling of the filaments between 4<Z/D<8.

POD modes at higher m-number typically shows m-filaments of positive and negative W with patterns similar to mode (k=1, m=3) and (k=1, m=4) as illustrated in Figure 11.

In general, the POD modes extracted at M=1.1 do not show evidence of shock and expansion patterns in the potential core of the jet (Ceglia et al. (2013).

M=0.3 M=0.9 M=1.1

k=1; m=0

Figure 9 First and second POD mode of axisymmetric mode m=0. Iso-surfaces of positive (yellow) and negative (blue) axial velocity component W.

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M=0.3 M=0.9 M=1.1

k=1; m=2

k=2; m=2

Figure 10 First and second POD mode of azimuthal mode m=2. Iso-surfaces of positive (yellow) and negative (blue) axial velocity component W.

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M=0.3 M=0.9 M=1.1

k=1; m=3

k=1; m=4

Figure 11 First and second POD mode of azimuthal mode m=3 and m=4. Iso-surfaces of positive (yellow) and negative (blue) axial velocity component W.

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CONCLUSIONS

This paper described an experimental investigation on compressible jets at high-speed regime by tomographic particle image velocimetry (TOMO PIV). Experiments are performed at M=0.3, 0.6 and 1.1 in a jet tomography facility. The paper focused on the 3D organization of the large scale motions across the end of the potential core, where there is a significant acoustic source. The patterns were objectively identified by applying azimuthal Fourier decomposition and POD to the 3D velocity data. The modal patterns were described based on pattern visualizations of the axial velocity, being the main contributor to the total fluctuating kinetic energy among the velocity components. The most energetic modes show energy peaks by the end of the potential core and beyond (Z/D>5). Energy minima are observed in the first part of the potential core (2.6<Z/D<5), also in the M=1.1 case, which is characterized by shock and expansion waves.

ACKNOWLEDGEMENTS

This research has been conducted as part of the ORINOCO project funded by the European Community’s Seventh Framework Program

REFERENCES

Alkislar MB, Krothapalli A, Butler GW (2007), The effect of streamwise vortices on the aeroacoustics of a Mach 0.9, Journal of Fluid Mechanics, 578:139–169.

Boersma BJ (2005), Large Eddy Simulation of the sound field of a round turbulent jet, Theoretical Computational Fluid Dynamics, 19:161-170.

Bogey C, Bailly C, Juve´ D (2003), Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES, Journal of Theoretical and Computational Fluid Dynamics, 16(4):273–297.

Ceglia G, Violato D, Tuinstra M, Scarano F (2013), High-resolution PIV analysis of compressibility effects in turbulent jets, 10th international symposium on Particle Image Velocimetry – PIV13, Delft, The Netherlands.

Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006), Tomographic particle image velocimetry, Experiments in Fluids, 41:933–947.

Freund JB (2001), Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9, Journal of Fluid Mechanics, 438:277-305.

Freund JB, Colonius T (2002), POD Analysis of Sound Generation by a Turbulent Jet, AIAA 2002-0072, 40th AIAA Aerospace Sciences Meeting and Exhibit, January 14-17, 2002/Reno, NV

Iqbal MO, Thomas FO (2007), Coherent structure in a turbulent jet via a vector implementation of the proper orthogonal decomposition, Journal of Fluid Mechanics, 571: 281-326.

Jordan P, Colonius T (2013), Wave packets and turbulent jet noise, Annual Review of Fluid Mechanics, 45:173-95. Jung D, Gamard S, George WK (2004), Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region, Journal of Fluid Mechanics, 514: 173-204.

Lynch KP, Thurow BS (2009), POD analysis of 3d-flow visualization images of a circular jetwith Reynolds number 9500, 39th AIAA Fluid Dynamics Conference, San Antonio, USA.

Sirovich L (1987), Turbulence and the dynamics of coherent structures. Part 1: Coherent structures, Quarterly of Applied Mathematics, Vol. XLV, 561-571.

Tinney CE, Glauser MN, Ukeiley LS (2008), Low-dimensional characteristic of a transonic jet. Part 1. Proper orthogonal decomposition, Journal of Fluid Mechanics, 612:107-141.

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Tinney CE, Ukeiley LS, Glauser MN (2008b), Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction, Journal of Fluid Mechanics, 615:53- 92.

Violato D, Scarano F (2011), Three-dimensional evolution of flow structures in transitional circular and chevron jets, Physics of Fluids, DOI: 10.1063/1.3665141.

Violato D, Scarano F (2013), Three-dimensional vortex analysis and aeroacoustic source characterization of jet core breakdown, Physics of Fluids, 25, 015112, DOI 10.1063/1.4773444.

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